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Surface cracks are commonly observed in coatings and films. When structures with coatings are subject to stretching, opening mode cracks are likely to form on the surface, which may further lead to other forms of damage, such as interfacial delamination and substrate damage. Possible crack forms include cracks extending towards the interface and channeling across the film. In this paper, a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension. The energy release rate and structural stress intensity factors can be obtained accordingly, and the effects of geometry and material features on fracture characteristics are investigated, with most crack patterns being confirmed as unstable. The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films. The results from the numerical model are compared with those obtained by the finite element method (FEM), and the accuracy of the theoretical results is demonstrated. [ABSTRACT FROM AUTHOR]

The operation modes for the proposed FCC-ee collider foresee a very small beam spot size and stored beam energies of up to 20.6 MJ in Z production. This necessitates a dedicated beam dumping system. To reduce the complexity of the system as well as to minimize the required space, an optimized, semi-passive system has been designed and is presented here. The beam dilution is done with a defocusing triplet structure, followed by passive beam diluter elements (spoilers). This greatly reduces the risk of possible dilution failure scenarios compared to an active dilution kicker-magnet system. The dump core itself is located ∼ 70 m downstream of the spoilers and is designed following the experience gained from the LHC dump. The dilution performance as well as the interaction effects responsible for the energy deposited in the spoiler, are directly related to the radiation length and the dimension of the device in beam direction. Materials for these spoilers have been studied extensively and key requirements have been identified using both Monte Carlo shower simulations and thermo-mechanical Finite Element Analysis. Even though the maximum temperature reached in the spoilers is well within the working temperature range of the material, the induced mechanical stresses can lead to material failure. Thermo-mechanical simulations have shown that the transversal beam shape plays a key role in the magnitude of mechanical stresses as a result of the beam impact and the abrupt temperature change. This problem is addressed in this paper and an optimized solution is presented. [ABSTRACT FROM AUTHOR]

The low-k/ultra-low-k (LK/ULK) dielectric materials are incorporated in the 40 nm technology node and beyond to reduce resistance and capacitance (RC) delays and improve chip performances. However, the LK/ULK integrity becomes critical in a flip-chip process because of the LK/ULK materials' higher porosity and fragility in mechanics. In this paper, we proposed a three-dimensional (3D) one-level global/local finite element model to study stresses and fracture behaviors in the chip with ULK dielectrics in the heating flip-chip process using SIMULIA ABAQUS software. The global model includes an effective thin layer that is equivalent to Cu/low-k multilayer interconnections. On the basis of stress analysis, the precracks at different locations of back-end of line (BEOL) were introduced to estimate the values of energy release rate (ERR) along the 3D crack fronts and the possible crack extension was discussed. Furthermore, the ERR affected by the ULK modulus, polyimide thickness and copper pillar diameter was investigated. The analysis reveals that the values of ERR are higher in upper layers of the BEOL and their values at interfaces of Cu/ULK are as much as two times than in ULK. The ERR reaches its maximum value under the edge of copper pillar with higher first principal stresses. The crack propagation becomes critical due to a quickly rising value of ERR when the polyimide (PI) thickness or the diameter of copper pillar is decreased. The study helps to understand the fracture behaviors in BEOL of an advanced chip during a packaging process. [ABSTRACT FROM AUTHOR]

The paper presents the results of the application of the refined calculation guidelines to the analysis of the stress-strain state and fracture resistance of the equipment elements of the NPP primary circuit system with WWER reactor, in particular, the cylindrical part and the zone of the reactor pressure vessel inlet nozzle, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft under the operating and emergency modes of thermomechanical loading. The calculation methodology is based on the use of the modern models and methods of solution to the nonlinear boundary tasks of non-isothermal thermal viscoplasticity and tasks of fracture mechanics using the refined mixed schemes of the finite element method with increased accuracy. They allow one to obtain reliable solutions to the tasks considering the deformation history of thermomechanical loading, modern concepts of fracture mechanics and approaches to the modeling of brittle-viscous fracture defects, irradiation swelling and creep of metal, as well as as the structural elements, under the conditions of elevated temperature, intensive neutron irradiation and nonstationary modes of thermomechanical loading. The authors obtained and analyzed the calculation results for the cylindrical part and zone of the inlet nozzle of the WWER-1000 reactor pressure vessel, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft using the proposed guidelines. The results imply the possibilities of the proposed recommendations and make it possible to analyze some general tendencies and features of the application of the refined calculation models to justify the strength and life extension of the NPP structural elements under investigation. [ABSTRACT FROM AUTHOR]

In this paper, the effect of creep-fatigue loading condition on crack tip deformation and stress fields of Grade 91 steel at 600 °C at crack initiation and growth is studied. By using finite element debond analysis method, creep-fatigue crack growth tests using C(T) specimens under various load ratios and hold times are simulated, and the effect of creep-fatigue load ratio and hold time on the crack opening profile, equivalent stress, crack-opening stress and triaxiality at crack initiation and growth is presented. It is found that the crack tip deformation and stress fields under tension–compression creep-fatigue loading are overall different from those under tension-tension creep-fatigue and pure creep loading, due to re-sharpening of the crack tip. [ABSTRACT FROM AUTHOR]

Crack growth leads to roller failure and damages other parts. The three-dimensional modeling of crack growth, the effect of different factors on the fatigue life of roller, and the effect of stress distribution are important factors that should be considered. The purpose of this paper is to investigate the failure and modeling of three-dimensional fatigue crack growth and fatigue life prediction of high chromium steel (HCS) rollers in hot rolling to minimize the failure of rollers by practical solutions. This article uses boundary element method for fatigue crack growth under the influence of stress field. The proposed method allows modeling each of the components involved separately in the contact area. As a result, this method is faster than finite element models with contact components. In this regard, the types and causes of cracks in the roller are analyzed with the effect of residual stresses on the roller. By selecting the HCS roller and sheet, modeling and stress analysis are performed by finite element method. This study includes the effect of crack growth factors such as load ratio, length, and initial crack angle. The results of the numerical model showed a good agreement with the results obtained in the field observations. [ABSTRACT FROM AUTHOR]

This paper is aimed at modeling the propagation of multiple cohesive cracks by the extended Voronoi cell finite element model or X-VCFEM. In addition to polynomial terms, the stress functions in X-VCFEM include branch functions in conjunction with level set methods and multi-resolution wavelet functions in the vicinity of crack tips. The wavelet basis functions are adaptively enriched to accurately capture crack-tip stress concentrations. Cracks are modeled by an extrinsic cohesive zone model in this paper. The incremental crack propagation direction and length are adaptively determined by a cohesive fracture energy based criterion. Numerical examples are solved and compared with existing solutions in the literature to validate the effectiveness of X-VCFEM. The effect of cohesive zone parameters on crack propagation is studied. Additionally, the effects of morphological distributions such as length, orientation and dispersion on crack propagation are studied. [ABSTRACT FROM AUTHOR]

The paper describes the computational aspects and numerical implementation of a two-scale cohesive surface methodology developed for analyzing fracture in heterogeneous materials with complex micro-structures. This approach can be categorized as a semi-concurrent model using the representative volume element concept. A variational multi-scale formulation of the methodology has been previously presented by the authors. Subsequently, the formulation has been generalized and improved in two aspects: (i) cohesive surfaces have been introduced at both scales of analysis, they are modeled with a strong discontinuity kinematics (new equations describing the insertion of the macro-scale strains, into the micro-scale and the posterior homogenization procedure have been considered); (ii) the computational procedure and numerical implementation have been adapted for this formulation. The first point has been presented elsewhere, and it is summarized here. Instead, the main objective of this paper is to address a rather detailed presentation of the second point. Finite element techniques for modeling cohesive surfaces at both scales of analysis (FE $$^2$$ approach) are described: (i) finite elements with embedded strong discontinuities are used for the macro-scale simulation, and (ii) continuum-type finite elements with high aspect ratios, mimicking cohesive surfaces, are adopted for simulating the failure mechanisms at the micro-scale. The methodology is validated through numerical simulation of a quasi-brittle concrete fracture problem. The proposed multi-scale model is capable of unveiling the mechanisms that lead from the material degradation phenomenon at the meso-structural level to the activation and propagation of cohesive surfaces at the structural scale. [ABSTRACT FROM AUTHOR]

Damage models are widely used to describe the ductile damage and fracture of metals. This paper proposes a new approach to determine the damage parameters of the Gurson-Tveergard-Needleman model, which uses a load-displacement curve coupled with finite element method. The load-displacement curve was obtained from a tensile test of a smooth tensile specimen and contained information about the damage and fracture behavior of the tested material. The principle of damage parameters identification is to minimize the deviation between experimental and simulated load-displacement curves by a hybrid particle swarm optimization. As a combination of particle swarm optimization and simulated annealing, the hybrid particle swarm optimization is an economical and effective algorithm to identify damage parameters. The identified damage parameters are also verified by testing and simulating deformation shapes of the smooth tensile specimen which is used for parameters determination. Tests and simulations of notched tensile specimens were carried out to discuss the transformability of the identified damage parameters. It is observed that the value of critical void volume fraction of the Gurson-Tveergard-Needleman model decreases with the increase of stress triaxiality. [ABSTRACT FROM AUTHOR]

This paper considers the thermodynamically substantiated derivation of the scalar and vector forms of the J-integral for the Biot elastic porous medium model representing a permeable deformable matrix saturated with a fluid, which is described as a double continuum and whose behavior is determined by coupled equations of elasticity and filtration theory. [ABSTRACT FROM AUTHOR]

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con-ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors (SIFs) in rotating disks containing three-dimensional (3D) semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop-erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen-trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as me-chanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature. [ABSTRACT FROM AUTHOR]

This paper investigated the mechanism of fracture in concrete due to the deflagration phenomenon. For this purpose, the electric discharge impulse crushing method was selected, with liquid nitromethane (NM) taken as the deflagration agent. Employing this technique, NM is set inside charge holes and initiated by electric discharge. The pressure generated by the deflagration of NM in a steel chamber was modeled using the Jones-Wilkins-Lee equation of state. The modeled and measured pressures agreed well and the applicability of the pressure model was validated. Then, assuming controlled splitting along the expected fracture surface in concrete, dynamic fracture process analysis (DFPA) based on two-dimensional dynamic finite element method was conducted. The results showed that fracture patterns predicted in the DFPAs agreed well with those obtained from experiments. The mechanism of fracture in concrete due to deflagration was then discussed in terms of the fracture process in the controlled splitting. Owing to stress interference from each charge hole, compressive stress zones (CSZs) formed above and below the middle regions between charge holes where maximum and minimum principle stresses were both in compression. The CSZs was found to be important in obtaining a flatter fracture surface in the case of controlled splitting. In conclusion, the proposed method was shown to be useful for the investigation of the fracture mechanism in the case of the use of deflagration agents and could be useful for the design optimization of such controlled splitting. [ABSTRACT FROM AUTHOR]

This paper studies propagation criteria in three-dimensional fracture mechanics within the extended finite element framework (XFEM). The crack in this paper is described by a hybrid explicit-implicit approach as proposed in Fries and Baydoun (Int J Numer Methods Eng, ). In this approach, the crack update is realized based on an explicit crack surface mesh which allows an investigation of different propagation criteria. In contrast, for the computation of the displacements, stresses and strains by means of the XFEM, an implicit description by level set functions is employed. The maximum circumferential stress criterion, the maximum strain energy release rate criterion, the minimal strain energy density criterion and the material forces criterion are realized. The propagation paths from different criteria are studied and compared for asymmetric bending, torsion, and combined bending and torsion test cases. It is found that the maximum strain energy release rate and maximum circumferential stress criterion show the most favorable results. [ABSTRACT FROM AUTHOR]

Asymmetric four point bend specimens are often used for determination mode II fracture toughness. Different corrections were proposed to classical solution of Stress Intensity Factors for this specimen. This paper provides a solution for a bi-material four point specimen with sub-interface crack. The solutions were obtained using Finite Element Analysis, and the effect of crack distance to interface, crack length and materials combination were investigated. [ABSTRACT FROM AUTHOR]

Recently, authors(Cao et al., Acta Aeronautica et Astronautica Sinica 25(5): 470–472, 2004) extended the singular crack element originally introduced by Wang et al. (Eng Fract Mech 37(6):1195–1201, 1990) for evaluating the stress intensity factors (SIFs). Extensive studies have proved the versatility and accuracy of the element. This study is to show the versatility of the element for piezoelectric materials. In this paper, electric potential and displacement fields near a crack tip of piezoelectric materials are first used to construct a finite element version for directly determining intensity factors of piezoelectric materials with cracks. A singular finite element is constituted and a new method to calculate intensity factors of piezoelectric materials with cracks is obtained without any post-processing procedures. Detailed derivations are given and the results obtained with present method are good agreement with those of theoretical results, the FEM data by ANSYS and singular electromechanical crack tip elements. The results to the different selections of the structural dimensions are carried out. Numerical examples demonstrate the accuracy and validity of the novel element of present method. [ABSTRACT FROM AUTHOR]

This paper considers isotropic and orthotropic nonlinear constitutive relations for brittle materials in the case of plane stresses. Numerical solution algorithms based on the finite-element method are developed. The resulting material models are incorporated in the PIONER software. The correctness of crack path determination is examined by solving a test problem of crack propagation. The isotropic model gives mesh-dependent results, whereas the orthotropic model provides an adequate solution. It is shown that solutions obtained for the isotropic model are close to those obtained by eliminating failed elements. [ABSTRACT FROM AUTHOR]

An analytical expression for the stress intensity factor related to a crack stemming from a blunted V-notch tip is put forward. The analysis is limited to mode I loading conditions, as long as the crack length is sufficiently small with respect to the notch depth. The proposed formula improves significantly the predictions of a recently introduced relationship, by considering a notch amplitude dependent parameter. Its values are estimated through a finite element analysis: different notch amplitudes, ranging from $$0^{\circ }$$ to $$180^{\circ }$$ , and different crack length to root radius ratios, ranging from 0 to 10, are taken into account. The evaluation of the apparent generalized fracture toughness according to equivalent linear elastic fracture mechanics concludes the paper. [ABSTRACT FROM AUTHOR]

The heat treatment of tire protection chains has a major influence on the final product because the high local stresses that arise during quenching may lead to material failure, i.e., quench cracks. The investigations presented in this paper aim at the identification of critical areas in the design of a tire chain link made of 50CrV4 (DIN 1.8159) steel. Parametric studies were conducted by means of finite element (FE) simulation. The FE model enables the calculation of the stress evolution in the chain link during heat treatment. The position of the cracks produced in laboratory quench experiments coincided with the position where the FE simulation model predicted the maximum tensile stress at the end of the quench. Hence, geometry optimization of the chain links is now possible by means of parametric FE studies aiming to minimize these tensile stresses. To identify the influence of the various input parameters on the calculated stress evolution during the quenching, a sensitivity analysis was performed. The influence of the mesh size, the heat transfer at the surface, and the thermo-mechanical properties of the material phases on the stress calculation was evaluated and trends were identified. Temperature measurements during quenching experiments were used to determine the heat transfer parameters. X-ray residual stress measurements on pre-defined positions after an instrumented laboratory quenching were used to validate the simulation results. [ABSTRACT FROM AUTHOR]

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place. [ABSTRACT FROM AUTHOR]

This paper develops an interaction integral method for extracting the T-stress of an interface crack in the materials with complex interfaces. In numerical computations, the interaction integral should be converted into an equivalent domain formulation to ensure numerical precision. It can be found that the present domain formulation does not contain any terms related to material interfaces, namely, the interaction integral is domain-independent for material interfaces. As a deduction, the present interaction integral can be used to solve the T-stress for a crack located on a curved interface effectively. Combined with the extended finite element method, the interaction integral method is employed to solve several interface crack problems. Good accuracy can be obtained for the interface fracture of a typical bimaterial strip. Meanwhile, it can be noted that the T-stress converges to a stable value only when the integral domain reaches up to an enough size. Since it is extremely difficult to select a large enough integral domain without any interfaces for the materials with complex interfaces, the domain-independence of the present interaction integral for interfaces is practical significant. Due to this point, the interaction integral method will become a quite reliable and convenient technique to solve the T-stress of an interface crack in the materials with complex interfaces. Finally, the interfacial fracture problem is investigated for several representative centrosymmetric structures formed by two constituent materials. [ABSTRACT FROM AUTHOR]

This paper proposes a numerical method to simulate hydrogen-assisted stress corrosion cracking, via coupled diffusion elastic-plastic finite element damage analyses based on phenomenological stress-modified fracture strain model. For validation, simulated results using the proposed method are compared with published experimental data of FeE 690T compact tension tests under air and hydrogen condition with various constant load-line displacement rates. The simulated results agree well with experimental data. [ABSTRACT FROM AUTHOR]

This paper developed 3D elastoplastic finite element analysis (FEA) models to investigate non-axisymmetric tubes neck spinning. The three-roller mandreless neck spinning process was simulated by commercial FEA software, MSC. Marc. The distribution of the transient von Mises stresses in the contact zone between the roller and the blank, and the equivalent plastic strains after spinning were obtained. The locations and causes of fractures were analyzed. The thickness distribution of the spun workpiece was investigated numerically and experimentally. It shows that during 3D non-axisymmetric tubes spinning, diametral elongation and fractures mostly occur at the opening end of workpiece, which considered as the primary location of defects. Fractures may also occur easily at the initial spinning area, which may be considered a secondary location of defects. The distributions of equivalent stresses and strains are non-uniform during both offset and oblique 3D non-axisymmetric tubes spinning. The maximum stress and strain values occur at the location where the biggest offset or inclination is induced, while the minimum values occur at the opposite location of 180° away from the maximum values. For the oblique tube, however, the strain distribution changes gradually along the axial direction, which is different from that of the offset tube. Thinning occurs during forward path spinning and thickening occurs during backward path spinning. Therefore, for multipath neck spinning processes, forward and backward paths should be applied alternately to avoid excessive thinning or thickening of workpiece. [ABSTRACT FROM AUTHOR]

The porous plasticity model (usually referred to as the Gurson-Tvergaard-Needleman model or modified Gurson model) has been widely used in the study of microvoid-induced ductile fracture. In this paper, we studied the effects of random voids on the porous plasticity model. Finite-element simulations were conducted to study a copper/tin/copper joint bar under uniaxial tension using the commercial finite-element package ABAQUS. A randomly distributed initial void volume fraction with different types of distribution was introduced, and the effects of this randomness on the crack path and macroscopic stress-strain behavior were studied. It was found that consideration of the random voids is able to capture more detailed and localized deformation features, such as different crack paths and different ultimate tensile strengths, and meanwhile does not change the macroscopic stress-strain behavior. It seems that the random voids are able to qualitatively explain the scattered observations in experiments while keeping the macroscopic measurements consistent. [ABSTRACT FROM AUTHOR]

The paper presents a model, based on nonlinear fracture mechanics, for analysing crack propagation in quasi-brittle materials, such as concrete. The work is limited to two-dimensions, and therefore, the fracture modes of interest are mode I (pure tension) and mode II (pure shear). The constitutive model has been implemented in the context of the finite element method using interface elements. The fracture is simulated through a discrete crack represented by the interface with a cohesive crack stress-separation relation derived from the model, which is based on a fracture criterion, together with a flow rule and a softening law. The model is used for simulating results from an experimental study on beams with centric and eccentric notches of high and normal strength concretes, and explaining other test results available in the literature. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to shed light on the effect of strain rate and viscoplastic deformation of bulk solder on the interfacial failure of lead-free solder joints. For this purpose, interfacial damage evolution and mode I fracture behavior of the joint were evaluated experimentally by performing stable fracture tests at different strain rates employing an optimized tapered double cantilever beam (TDCB) design. The viscoplastic behavior of the solder was characterized in shear, and the constitutive parameters related to the Anand model were determined. A rate-independent cohesive zone damage model was identified to best simulate the interfacial damage progression in the TDCB tests by developing a three-dimensional (3D) finite-element (FE) model and considering the viscoplastic response of the bulk solder. The influence of strain rate on the load capability and failure mode of the joint was clarified by analyzing the experimental and simulation results. It was shown how, at the lower strain rates, the normal stress generated at the interface is limited by the significant creep relaxation developed in the bulk solder and thus is not sufficiently high to initiate interfacial damage, whereas at higher rates, a large amount of the external energy is dissipated into interfacial damage development. [ABSTRACT FROM AUTHOR]

Design and manufacture of composite test specimens with two embedded delaminations subjected to transverse tension is described in this paper. The behaviour of the specimens has been investigated through experimental testing and finite element analyses. Fracture mechanics approaches were applied to predict the initiation and growth of delaminations and the degradation of the load carrying capacity of the specimens. Models were generated in the FE software programs MSC.Nastran and Abaqus. The MSC.Nastran model was used to calculate strain energy release rates employing a crack tip element methodology. The Abaqus model was evaluated using the virtual crack closure technique. The accuracy of numerical solutions was established by qualitative and quantitative comparisons with the experimental measurements, the results obtained from the ultrasonic non-destructive inspections and microscopic examination. It was shown that fracture mechanics can be used to accurately predict the failure initiation locations and failure loads of composite specimens containing multi-level delaminations. [ABSTRACT FROM AUTHOR]

This paper presents a new intrinsic enriched element free Galerkin method (EFGM) criterion for the simulation of multiple interacting crack problems. The principle attraction of the proposed criterion lies in its ability to handle multiple cracks of equal/unequal lengths. According to this proposed criterion, few modifications are made in standard intrinsic enriched EFGM criterion to solve multiple interacting cracks lying on the same as well as on the opposite face under plane stress conditions. The values of mode-I and mode-II stress intensity factors have been evaluated using domain based interaction integral approach. The modeling capabilities and accuracy of the proposed criterion has been demonstrated by comparing the results with those obtained by FEM. The proposed enrichment criterion has been found quite capable in analyzing crack growth as well as equal or unequal size multiple cracks. [ABSTRACT FROM AUTHOR]

The concept of a stress singularity is a cornerstone of modern fracture mechanics. A new mode of stress singularity, the out-of-plane singular mode or K O mode, was recently identified for V-shaped notches subjected to in-plane loading. This new mode is coupled with the shear mode and related to Poisson’s effect. The previous studies based on the first order plate theory focused on the derivation of a characteristic equation describing the strength of this singularity and provide no information regarding the intensity, extent and relevance of this mode to practical problems. This paper aims to fill this gap. The approach utilises the 3D finite element method and a standard regression technique for characterisation of the notch singular modes. A comprehensive study of the influence of Poisson’s ratio, plate thickness and notch opening angle on the value of the notch stress intensity factor associated with this mode is conducted for infinite plates. Additionally, to demonstrate the relevance of this new singular mode to practical problems an investigation of the out-of-plane mode and associated three-dimensional effects are presented for the case of a welded lap joint. Main areas of further research are also identified. [ABSTRACT FROM AUTHOR]

Three different effects control the influence of the loading rate on structural response: creep of bulk material, rate dependency of growing microcracks and structural inertia. The first effect is important only at extremely slow loading rates whereas the second and third effects dominate at higher loading rates. In the present paper, a rate sensitive model, which is based on the energy activation theory of bond rupture, and its implementation into the microplane model for concrete are discussed. It is first demonstrated that the model realistically predicts the influence of the loading rate on the uniaxial compressive behaviour of concrete. The rate sensitive microplane model is then applied in a 3D finite element analysis of the pull-out of headed stud anchors from a concrete block. In the study, the influence of the loading rate on the pull-out capacity and on the size effect is investigated. To investigate the importance of the rate of the growing microcracks and the influence of structural inertia, static and dynamic analyses were carried out. The results show that with an increase of the loading rate the pull-out resistance increases. For moderate loading rates, the rate of the microcrack growth controls the structural response and the results of static and dynamic analysis are similar. For very higher loading rates, however, the structural inertia dominates. The influence of structural inertia increases with the increase of the embedment depth. It is shown that for moderately high-loading rates the size effect becomes stronger when the loading rate increases. However, for very high-loading rate the size effect on the nominal pull-out strength vanishes and the nominal resistance increases with an increase of the embedment depth. This is due to the effect of structural inertia. [ABSTRACT FROM AUTHOR]

This paper presents a new method for predicting the stress intensity factors around a partly circumferential elliptical surface crack in a pipe. The solution is applicable to structures with both double and single curvature. The technique involves a conformal transform in conjunction with a semi-analytical approach that uses a finite element model to obtain the stress distribution in the undamaged structure. By using an indirect methodology, the model development is simplified and the analysis time is minimised. As such a coarse mesh can be used to obtain solutions for multiple crack geometries. Three examples are presented to verify this methodology. They include a partly circumferential elliptical crack under uniform tension, a pipe subject to a residual stress field, and a problem involving double curvature. For simple loading the solution compares with other published solutions to within 5% for an external crack, and to within 15% for an internal crack. For more complex loading conditions the majority of the solutions were within 5% of other published results at the deepest point, and most solutions at the surface agreed to within 15%. For the problem involving double curvature, the solutions agreed to within 4% for an internal crack, and 15% for an external crack. [ABSTRACT FROM AUTHOR]

Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE) analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plasticJand crack tip stresses for a plate with a through-thickness crack and semi-elliptical surface crack under positive biaxial loading. For the plate with a through-thickness crack, plate thickness and relative crack length are systematically varied, whereas for the plate with a semi-elliptical surface crack, the relative crack depth and aspect ratio of the semi-elliptical crack are systematically varied. It is found that the reference stress based approach for uniaxial loading can be applied to estimateJunder biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected for positive biaxial loading, and thus elastic-plasticJfor a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front. [ABSTRACT FROM AUTHOR]

The stress intensity factor is a traditional topic in mechanics and there have been many solutions for many different cases. The closed frictional crack problem has been modeled in the rock mechanics field where fractures are mostly under compression. Further, the effect of finite plate dimensions under biaxial loading has not been considered in the literature. The key contribution of the present paper is to evaluate the effect of the crack length to plate width ratio on the mode I and II stress intensity factors (SIF) of a central slant crack with frictional surfaces in plates with biaxial loading of different patterns, i.e. tension-tension, tension-compression, compression-tension or compression-compression. A plane strain elastic two-dimensional finite element analysis was adopted. Crack length to plate width ratios equal to 0.1, 0.3 and 0.5 with biaxial ratios from -1 to 1, crack angles from 0° to 90° and friction coefficients from 0 to 1 were considered. Contact regimes and the effect of the crack length to plate width ratio were found dependent on biaxial ratio and pattern, friction coefficient and crack angle. [ABSTRACT FROM AUTHOR]

A combined analytical and numerical method is proposed for the determination of the weight functions of stress intensity factors of cracks in an arbitrary three-dimensional elastic body. Having defined the weight functions for a given geometry of a structure, the stress intensity factors for arbitrary loading conditions can be obtained by a simple inner product of the weight function and a traction vector. Traditionally weight functions are defined in the two ways; the one is defined by the hyper-singular term of the eigen-function expansion of the displacement field of a cracked body, and the other is defined by the variation of displacement field with respect to a virtual extension of a crack. In the present paper, the weight functions for stress intensity factors are defined by applying the Maxwell-Betti's reciprocal theorem to an original problem and the auxiliary problems subjected to three kinds of force-couples acting on the crack surfaces near the limiting periphery of an arbitrary three-dimensional crack. In the present formulation, weight functions can be calculated by using a general-purpose finite element code combined with analytical expressions near the condensation point, where hyper-singularities exist. The validity of the method is confirmed by two- and three-dimensional illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper an incremental constitutive theory for the deformation due to switching in ferroelectrics is applied to predict the fracture toughness anisotropy in these materials after mechanical poling. Mechanical poling of an initially unpoled specimen differs from electrical poling in that only mechanical stresses are applied to the material. Therefore, no electrical polarization can develop. After mechanical poling, for example by a uniaxial applied stress, the fracture toughness of a ferroelectric ceramic for cracks running parallel or orthogonal to the poling direction will differ. Finite element computations of the steady crack growth process have been carried out to quantify these differences. Results are generated for a range of constitutive properties for three crack growth directions with respect to the initial mechanical poling direction. The results are discussed in relation to available experimental data and to the toughness anisotropy due to electrical poling. [ABSTRACT FROM AUTHOR]

The effect of out-of-plane constraint associated with a thickness on the toughness of three-dimensional bodies is a primary concern in fracture mechanics. The J - Δ σ approach has been shown to be capable of quantifying crack tip constraint loss in high and low constraint geometries using a deformation parameter, J / z σ o . The present study is motivated to use the parameter to assess the nature of out-of-plane constraint loss under Mode-I loading in a deeply cracked compact tension (CT) specimen. The assessment focuses on the variation in crack tip stress fields across the specimen thickness, which was examined through finite element analysis of full-field CT models in comparison with two-dimensional plane strain and plane stress solutions to identify the constraint loss pattern. The models with a sharp crack tip were constructed using quadratic brick elements and subjected to a displacement-controlled loading that corresponded to a limit load analysis. The results show that the state of three-dimensional stress fields in CT specimens departs from a plane strain condition at the midplane to a plane stress field near the free surface. Using the parameter J / z σ o , the loci of out-of-plane constraint loss in different specimen thicknesses subjected to varying deformation levels were unified into a single curve, and thus verifying the capability of the J - Δ σ approach to characterize the out-of-plane constraint loss in high constraint geometries of deeply cracked CT specimens. [ABSTRACT FROM AUTHOR]

The finite element model and fracture mechanic theory are applied to analyze the contact stress and fatigue crack growth (FCG) path in three dimensions for a transmission shaft, which owns the initial crack and runs with the periodic load. The study found that the periodic load generates a non-proportional stress intensity factor history (SIF) output in the root of the splines. A modified method based on Hertz theory and AGMA (American Gear Manufacture Association) standard is utilized to analyze contact stress with considering the crack growth. From this, it is feasible to predict FCG path in three dimensions for a cracked component. The comparison between the simulation and experiment illustrates that the crack growth path is sensitive to the location and magnitude of loads. Contact regions of stress and fracture mechanic parameters should be deeply analyzed and known before predicting FCG path in three dimensions. [ABSTRACT FROM AUTHOR]

Based on the crack mechanism of hot forming, the causes of cracks occurring during the hot forming of complex structural parts were investigated in this study. High temperature flow stress model of ultrahigh strength steel (UHSS) BR1500HS was established using the true stress-strain curves of BR1500HS in high-temperature tensile. A finite element model (FEM) was built to investigate the causes of defects in hot forming, particularly the necking occurring at the end parts in plan stress status. Then, hot forming process and structure optimizing methods were proposed. According to the results of numerical simulation, it can be concluded that the indirect hot forming process can avoid forming defects and optimize preforming drawing height to 24.5 mm. Through changing the end size of blank to control the metal flow, crack occurring at the end of parts can be solved, since the material in two-way tensile stress state can flow compensation in one direction and therefore reduce the flow resistance. The experimental results are in good agreement with numerical simulation results, which indicates that the proposed method can avoid defects and meet the design requirements. [ABSTRACT FROM AUTHOR]

The crack characterization in a pre-cracked aluminum specimen is investigated in this study using the grid method. The images of this grid are analyzed to provide the crack tip location as well as the displacement and strain fields on the surface of the specimen during a tensile test. Experimental data are used to calculate the energy release rate with the compliance method A fracture analysis is also performed using the invariant M $$\uptheta $$ integral in which both real and virtual displacement fields are introduced. This integral is implemented in the finite element software Cast3M. Both approaches give similar results in 2D case. [ABSTRACT FROM AUTHOR]

The paper is concerned with regularly structured solids. A two-stage solution is proposed for the nonlinear problem of fracture mechanics where branching or kinking of an initial mixed-mode crack is possible. First, the kink and branch angles are found, and then the critical fracture parameters for chosen directions are determined; in so doing, necessary and sufficient fracture criteria of the Neuber-Novozhilov type are used respectively. The critical fracture parameters (the lengths of prefracture and loads) are found with a modified version of the classical Leonov-Panasyuk-Dugdale model for prefracture zones confined in rectangles along crack branches. Simple expressions for the critical fracture parameters are derived using stress intensity factors for cracks with infinitesimal branches and for those with a branch on which normal and shear stress simulative of the plastic zone are specified. The stress intensity factors for a branched crack are obtained from solving the problem of uniaxial tension of a plate with a double-symmetric crack branch by the finite-element method. The stress intensity factors are calculated for mode I and II cracks in relation to the branch angle. [Copyright &y& Elsevier]

Chip separation is an important issue in finite element method (FEM)-based simulation of the cutting process owing to its significant impact on the predicted chip formation, as well as on the temperature and stress distributions. Typically, the chip separation criteria and the arbitrary Lagrangian–Eulerian (ALE) method have been utilized in chip formation simulations. This study aimed to evaluate the chip separation criterion and the ALE method in terms of chip formation, cutting force, cutting temperature, and stress distribution. Particularly, the effective plastic strain criterion and the failure-zone-assisted and ALE methods were utilized to model the orthogonal cutting of Inconel 718 alloy. Furthermore, experimentations were performed, and the results of FEM predictions were compared with the experimentally measured results. In general, ALE method was more consistent with the experiment. The ESPC method does not seem to handle chip shape and cutting temperature well, while the FZA method may not be suitable for predicting surface stress due to the deformation and failure of the material concentrated in the fail assist area. [ABSTRACT FROM AUTHOR]

Finite element analysis is a popular method used to characterize crack tip stress and strain fields in fracture mechanics problems. In a constraint-based elastic-plastic fracture mechanics, the crack tip stress and strains are essentially dependent on the accurate crack tip finite element configuration. Typical finite element software does not provide control of node and elemental numbering order and sequence which caused difficulty to examine different crack configuration state of stress–strain using automated post-processing codes. A method to automate the creation of finite element mesh of arbitrary lengths and shapes of standard and nonstandard fracture mechanics geometries using a geometric progression technique is described. A list of equations was proposed to develop nodal and elemental model data that represented a defined region of a cracked geometry. Assembly of the regions produced a finite element mesh representing a fracture mechanics cracked geometry which can be incorporated into a typical finite element program. The approach can eliminate the modeling processes of finite element of cracked specimens and offers the ability to control the nodal and elemental numbering system to allow systematic stress and strain elucidation for large degrees of freedom mesh and history-dependent incremental plasticity crack tip analysis. The approach used to develop the finite element mesh was discussed, and examples of the finite element mesh generated by the approach were compared to established two-parameter elastic-plastic fracture mechanics results. Finally, the algorithm codes used to develop the cracked models are supplied as supplementary files to interested users. [ABSTRACT FROM AUTHOR]

A series of specimens made from transparent casting resin, each with a spherical pore at the centre of specimen were tested in a polyaxial stress state with different stress ratios ( σ x / σ y ) between the lateral (the intermediate principal stress, σ x ) and the axial (the major principal stress, σ y ) loads, and the minor principal stress ( σ z ) was equal to 0, i.e., biaxial compression. The experimental results revealed the dramatic influence of the intermediate principal stress on the mechanics of 3D crack growth from a spherical pore. In uniaxial compression, the initial spherical pore produces several differently oriented wing cracks which are relatively short, smaller than the pore diameter (referred to as wing crack wrapping). In biaxial compression even with relatively low intermediate principal stress, a large wing crack is formed growing to an extent sufficient to split the specimen. The threshold for the intermediate principal stress separating these two regimes of wing crack growth is found to be 8.5% of the major principal stress. The results obtained from finite element method modelling show that with the intermediate principal stress above this threshold the directions of most of the secondary principal stresses (tensile) along the lateral surface of the initial pore are roughly perpendicular to the intermediate principal compressive stress direction. For the intermediate principal stress below the threshold, the directions of the secondary principal tensile stresses near the lateral surface of the initial pore are distributed in radial directions with respect to the initial pore. Results of numerical modelling also show that when transition is made from spherical pore to oblate pores, this threshold increases. [ABSTRACT FROM AUTHOR]

Sudden failure and rupture of the tissue is a rare but serious short-term complication after the mitral valve surgical repair. Excessive cyclic loading on the suture line of the repair can progressively damage the surrounding tissue and finally cause tissue rupture. Moreover, mechanical over-tension, which occurs in a diseased mitral valve, gradually leads to tissue floppiness, mitral annular dilation, and leaflet rupture. In this work, the rupture mechanics of mitral valve is studied by characterizing the fracture toughness exhaustion of healthy tissue. Results of this study show that fracture toughness of the posterior mitral valve is lower than its anterior counterpart, indicating that posterior tissue is more prone to failure. Moreover, the decrease in fracture toughness by increasing the number of fatigue cycles shows that excessive mechanical loading leads to progressive failure and rupture of mitral valve tissue within a damage accumulative process. [ABSTRACT FROM AUTHOR]

We formulate mathematical models for the evaluation of the lifetime of plates with systems of cracks under the action of long-term force loads in the presence of high temperatures and corrosive media. These models are based on the use of the well-known main mechanisms of propagation of creep cracks, corrosion fracture, and the first law of thermodynamics (balance of energy components and rates of their changes) for a metal plate containing a system of macrocracks and subjected to the action of long-term tension and corrosive media at high temperatures. We consider the case of a double-periodic system of cracks. [ABSTRACT FROM AUTHOR]

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson-Tvergaard-Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value. [ABSTRACT FROM AUTHOR]

Micro-cracks in ferritic steel often originate from broken or debonded carbide particles, or from cleavage of the ferrite matrix. Experiments in literature show that dislocation pile-ups at grain boundaries or particles predominantly induce micro-cracks in ferritic steel. On the other hand, the ferrite can also arrest nucleated micro-cracks owing to local plastic deformations which reduce the stresses at the crack tip. In the present study, the competition between these mechanisms is investigated by cell model simulations using effective gradient plasticity (scalar gradient plasticity) for the ferrite. This theory allows to model the dislocation pile-up by suitable interface conditions. Potential cleavage of the ferrite or failure of the carbide is modelled by a cohesive zone. Parameter studies are performed with respect to the size of the particle and the strengths of ferrite and carbide. [ABSTRACT FROM AUTHOR]

By introducing the shape functions of virtual node polygonal (VP) elements into the standard extended finite element method (XFEM), a conforming elemental mesh can be created for the cracking process. Moreover, an adaptively refined meshing with the quadtree structure only at a growing crack tip is proposed without inserting hanging nodes into the transition region. A novel dynamic crack growth method termed as VP-XFEM is thus formulated in the framework of fracture mechanics. To verify the newly proposed VP-XFEM, both quasi-static and dynamic cracked problems are investigated in terms of computational accuracy, convergence, and efficiency. The research results show that the present VP-XFEM can achieve good agreement in stress intensity factor and crack growth path with the exact solutions or experiments. Furthermore, better accuracy, convergence, and efficiency of different models can be acquired, in contrast to standard XFEM and mesh-free methods. Therefore, VP-XFEM provides a suitable alternative to XFEM for engineering applications. [ABSTRACT FROM AUTHOR]

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening-softening-hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (ΔK), load ratio (R), number of cycles (N), plastic compressibility (α) and material softening on near tip deformation, stress-strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on ΔK, R, N, α and material softening. For both hardening and hardening-softening-hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress-strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study. [ABSTRACT FROM AUTHOR]

An effective approach to the simulation of crack-type fracture is developed based on the semi-analytical finite element method. Algorithms for determining the parameters of fracture strength for elastic bodies of revolution and prismatic bodies under non-stationary force loading of different intensity and duration are proposed. The energy approach based on the application of a special prismatic and ring finite elements with crack under dynamic loading are used to calculate the fracture parameters. The efficiency of the algorithms is estimated. [ABSTRACT FROM AUTHOR]

The non-uniform friction and thermal stress in the mold are important as causes of the transverse cracks around strand corner. To analyze the stress distribution features around strand corner, a three-dimensional thermo-elastoplastic finite-element mold model with different corner structures (right-angle, big-chamfer, multi-chamfer, and fillet) was established. The temperature field in the mold was indirectly coupled through a three-dimensional fluid flow and heat transfer model. In addition, the non-uniform mold friction stress loaded on the strand surface was calculated through a friction model. The results show that the stress distribution on the shell is similar to the temperature distribution. The stress concentration appears in the strand corner and the lower part of wide face. The friction stress enhances the corner stress around the edge of the air-gap. For chamfered molds, the stress around the corner between the wide face and chamfer face is larger than that between the narrow face and chamfer face. Around the corner region, both the stress peak and the area of the large stress zone of the right-angle strand are the largest, while those of big-chamfered, multi-chamfered, and fillet strands decrease in that order. The stress peak position of the chamfered strands is closer to the mold exit than that of the right-angle strand. Compared with the use of the right-angle mold, the application of chamfered molds is able to reduce the stress concentration around the strand corner. [ABSTRACT FROM AUTHOR]